Data.Number.ER.Real.Approx.Interval

This module defines an arbitrary precision interval type and most of its interval arithmetic operations.

Documentation

data ERInterval base

Type for arbitrary precision interval arithmetic.

Constructors

ERIntervalEmpty

usually represents computation error (top element in the interval domain)

ERIntervalAny

represents no knowledge of result (bottom element in the interval domain)

ERInterval

Fields

erintv_left :: base

erintv_right :: base

Instances

Typeable1 ERInterval

ERRealBase b => Eq (ERInterval b)

ERRealBase b => Fractional (ERInterval b)

Data base => Data (ERInterval base)

ERRealBase b => Num (ERInterval b)

ERRealBase b => Ord (ERInterval b)

ERRealBase b => Show (ERInterval b)

Binary a => Binary (ERInterval a)

(ERRealBase b, HTML b) => HTML (ERInterval b)

(ERRealBase b, RealFrac b) => ERIntApprox (ERInterval b)

(ERRealBase b, RealFrac b) => ERApprox (ERInterval b)

(ERRealBase b, RealFrac b) => ERApproxElementary (ERInterval b)

normaliseERInterval :: ERRealBase b => ERInterval b -> ERInterval b

convert to a normal form, ie:

• no NaNs as endpoints

• l <= r

• no (-Infty, +Infty)

intervalTimesInner :: ERRealBase b => ERInterval b -> ERInterval b -> ERInterval b

Multiply two real approximations, assuming the approximations are inner as opposed to outer:

• outer: the approximation contains all the number(s) of interest * inner: all numbers eligible for the approximation are numbers of interest

intervalPlusInner :: ERRealBase b => ERInterval b -> ERInterval b -> ERInterval b

Add two real approximations, assuming the approximations are inner as opposed to outer:

• outer: the approximation contains all the number(s) of interest * inner: all numbers eligible for the approximation are numbers of interest

intervalDivideInner :: ERRealBase b => ERInterval b -> ERInterval b -> ERInterval b